Surface Area of a Triangular Prism
The Surface Area of a Triangular Prism is divided into two parts Lateral Surface Area and Total Surface Area
Lateral Surface Area (LSA) of a Triangular Prism:
The lateral surface area (LSA) of a triangular prism is the total area of all its sides excluding the top and bottom faces. The formula to calculate the lateral surface area is given by:
Lateral Surface Area (LSA) = (s1 + s2 + h)L
Here, s1, s2, and s3 are the lengths of the edges of the base triangle, and L is the length of the prism.
For a right triangular prism, the formula is:
Lateral Surface Area = (s1 + s2 + h)L
OR
Lateral Surface Area = Perimeter × Length
Here, (h) represents the height of the base triangle, (L) is the length of the prism, and s1 and s2 are the two edges of the base triangle.
Total Surface Area (TSA) of a Triangular Prism
The total surface area (TSA) of a triangular prism is found by adding the area of its lateral surface (the sides) and twice the area of one of its triangular bases. For a right triangular prism, where one of the bases is a right-angled triangle, the formula for the total surface area is given by:
Total Surface Area (TSA) = (b × h) + (s1 + s2 + s3) L
Here, s1, s2, and s3 are the edges of the triangular base, (h) is the height of the base triangle, (l) is the length of the prism, and (b) is the bottom edge of the base triangle.
For a right triangular prism specifically, the formula simplifies to:
Total Surface Area = (s1 + s2 + h) L + b × h
Where,
- b is the bottom edge of the base triangle.
- h is the height of the base triangle.
- L is the length of the prism.
- s1 and s2 represent the two edges of the base triangle.
- bh represents the combined area of the two triangular faces.
- (s1 + s2 + h) L represents the combined area of the three rectangular side faces.
This formula essentially accounts for the areas of all the faces (rectangular and triangular) of the prism, providing a comprehensive measure of its total surface area.
Triangular Prism
Triangular Prism is a three-dimensional geometric shape with two identical triangular faces connected by three rectangular faces. It is one of the classifications of prism. It is named a triangular prism because it has a triangle across its cross-section.
This article covers the meaning of prism and triangular prism, the properties of the prism, the formula of a triangular prism, and the net of a triangular prism. We will also see the types of triangular prism on the basis of uniformity and alignment and verify Euler’s rule for triangular prism.
Table of Content
- What is Prism?
- What is a Triangular Prism?
- Types of Triangular Prism
- Triangular Prism Faces Edges Vertices
- Surface Area of a Triangular Prism
- Volume of Triangular Prism
Contact Us